AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4

AP State Syllabus AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 Textbook Questions and Answers.

AP State Syllabus 7th Class Maths Solutions 8th Lesson Congruency of Triangles Exercise 4

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4

Question 1.
Which congruence criterion do you use in the following?
(i) Given :AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 1

(ii) Given: ZX = RP
RQ = ZY
∠PRQ ≅ ∠XZY
So, ΔPQR ≅ ΔXYZ
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 2

(iii) Given: ∠MLN ≅∠FGH
∠NML ≅ ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 3

(iv) Given: EB = DB . D
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 4
Solution:
(i) S.S.S congruence
(ii) S.A.S congruence
(iii) A.S.A congruence
(iv) By R.H.S congruence

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4

Question 2.
You want to show that ΔART ≅ ΔPEN,
(i) If you have to use SSS criterion, then you need to show
(a) AR= (b) RT = (c) AT=
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 5
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 6
Solution:
(i) (a) AR = PE
(b) RT = EN
(c) AT = PN

(ii) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(a) RT = ? and (ii) PN = ?
Solution:
(a) RT = EN and
(ii) PN = AT

(iii) If it is given that AT = PN and you arelo use ASA criterion, you need to have
(a)? (b)?
Solution:
a) ∠A = ∠P
b) ∠T = ∠N

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4

Question 3.
You have to show that ΔAMP ≅ ΔAMQ. In the following proof. supply the missing reasons.

Steps Reasons
(i) PM = QM (i) …………….
(ii) ∠PMA ≅ ∠QMA (ii) …………….
(iii) AM = AM (iii) …………….
(iv) ∆AMP ≅ ∆AMQ (iv) …………….

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 7
Solution:

Steps Reasons
(i) PM=QM (i) Given side
(ii) ∠PMA ≅ ∠QMA (ii) Given angle
(iii) AM=AM (iii) Common side
(iv) ∆AMP ≅ ∆AMQ (iv) A.A.S criterion

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4

Question 4.
In ΔABC’, ∠A = 30°, ∠B = 40° and ∠C = 110°
In ΔPQR, ∠P = 30°, ∠Q = 40°and ∠R = 110°
A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is hejustified? Why or why not?
Solution:
The student Is not correct.
AAA is not a congruency criteria.
Triangles with same corresponding angles can have different sizes.

Question 5.
In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ΔRAT? ≅ ?
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 8
Solution:
ΔRAT ≅ ΔWON

Question 6.
Complete the congruence statement.
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 9
Solution:
ΔABC ≅ ?
ΔABC ≅ ΔABT

ΔQRS ≅ ?
ΔQRS ≅ ΔTPQ

AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4

Question 7.
In a squared sheet, draw two triangles of equal areas such that
(i) the triangles are congruent.
(ii) the triangles are not congruent.
What can you say about their perimeters?
Solution:
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 10
i) ΔABC ≅ ΔPQR
Since AB = PQ
∠B = ∠Q
BC = QR (Perimeter is same)

ii) Area of ΔXYZ = \(\frac { 1 }{ 2 }\) x 10 x 4 : 20 sq.units.
Areas of ΔLMN= \(\frac { 1 }{ 2 }\) x 8 x 5=2Osq. units
But ΔXYZ and ΔLMN are not congruent.
(Perimeter is different)

Question 8.
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 11
Solution:
We need to know that BC = QR. Here we use A.S.A criterion.

Question 9.
Explain, why
ΔABC ≅ ΔFED.
AP Board 7th Class Maths Solutions Chapter 8 Congruency of Triangles Ex 4 12
Solution:
∠B = ∠E
BC = ED
∠C = ∠D by angle sum property.